If \[2x^2 - 3x - m \] is divisible by (x - 3) what is m?
A. -18
B. -9
C. -6
D. 9
E. 18
Could someone show me how to prove that the correct answer is the option D? I'd really appreciate it. Thanks.
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If 2x^2 - 3x - m is divisible by (x - 3) what is m?
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Sionainn@PrincetonReview
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Essentially we need to factor 2x^2 -3x -m and they tell us one of the factors is (x - 3)
When we're factoring picture doing FOIL in reverse. So if one of the first terms is x then the other would need to be 2x so that their product is 2x^2. So at this point we have it factored as
(x - 3) (2x___)
We also know the outer and inner term would need to have a sum of -3x. And with what we have factored the inner terms would have a product of - 6x (-3*2x). So the outer terms have to have a product of 3x. For the outer terms to have a product of 3x, the missing number would have to be 3, so it would factor to
(x - 3)(2x + 3)
Now multiply these to get
2x^2 -3x - 9
So we know m = 9 and D is correct.
While you could also plug in values for x, in this case you would likely need to try a few different numbers to narrow the answer choices down to one, so algebra is more efficient on this one.
Take care,
Sionainn
When we're factoring picture doing FOIL in reverse. So if one of the first terms is x then the other would need to be 2x so that their product is 2x^2. So at this point we have it factored as
(x - 3) (2x___)
We also know the outer and inner term would need to have a sum of -3x. And with what we have factored the inner terms would have a product of - 6x (-3*2x). So the outer terms have to have a product of 3x. For the outer terms to have a product of 3x, the missing number would have to be 3, so it would factor to
(x - 3)(2x + 3)
Now multiply these to get
2x^2 -3x - 9
So we know m = 9 and D is correct.
While you could also plug in values for x, in this case you would likely need to try a few different numbers to narrow the answer choices down to one, so algebra is more efficient on this one.
Take care,
Sionainn
BA - Stanford University, MPP - Harvard University
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Scott@TargetTestPrep
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We can solve this problem using the factor theorem, which states that:M7MBA wrote:If \[2x^2 - 3x - m \] is divisible by (x - 3) what is m?
A. -18
B. -9
C. -6
D. 9
E. 18
If P(x) is a polynomial function and (x - a) is a factor of P(x), then P(a) = 0.
So we can let P(x) = 2x^2 - 3x - m. Since (x - 3) is a factor of P(x), P(3) must be 0. Therefore,
P(3) = 2(3)^2 - 3(3) - m = 0
18 - 9 - m = 0
9 = m
Answer: D
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